Good question. While some people rather rashly claim these as "Buddhism teaches ...." simply because it is a Theravadin teaching, it's worth noting that it is rather late even in the Theravada. I have never seen any mention of them, or anything even close, in other schools (eg. of the so-called 18 schools; so this includes the Agamas) or Mahayana teachings. Though, would be interested in any clues that they may be there.

Further down in the linked text the Mahathera mentions various suttas that the commentators used to put together this 5-fold niyama system. He also said it was done mainly to refute the creator-god notion.

Why the authority of this niyama scheme should be questioned as fully "Buddhist" puzzles me. Mahayana is chock full of texts by Nagarjuna, Dharmakirti, Asanga et al, which are accepted as the simple unpacking or organizing of Buddha's teachings. So why not give these non-Mahayana commentators the same respect?

Basically, there is not even one buddha, only great wisdom. Bodhisattva Hsuan Hua